Your understanding is incorrect.
The requirement is roughly paraphrasing.. ..a position that a US person is not available to fulfill the requirements for, based on the prevailing wage..".

There appear to be plenty of Americans available to work live-in.

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Does your response mean that you believe that this would not be a route to obtaining a work visa, due to plenty of Americans being available to take a live-in position? I am interested in whether there is any mileage in trying for a work visa through this method.

I was presuming (maybe incorrectly) that US citizens may not be so willing to take a live in postion, possibly preferring to earn a wage

Work visas are for hard to fill positions, not sure the position that you're after, qualifies. But you can give it a shot by contacting the attorneys for your potential employer who would petition you and initiate the work visa process.

Work visas are for hard to fill positions, not sure the position that you're after, qualifies. But you can give it a shot by contacting the attorneys for your potential employer who would petition you and initiate the work visa process.

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Thanks. I guess my main question is whether it would be possible to obtain a visa for a position that is more of a work exchange than paid employment. Is the level of wage an important consideration for obtaining a work visa?